n-representation-finite algebras and twisted fractionally Calabi-Yau algebras

Details n-representation-finite algebras and twisted fractionally Calabi-Yau algebras n-representation-finite algebras and twisted fractionally Calabi-Yau algebras

2009-08-25

arxiv.org/abs/0908.3510v2

Mathematics

Representation Theory

15 pages, more detailed proofs and examples are added

Scientific paper

In this short paper, we study $n$-representation-finite algebras from the viewpoint of the fractionally Calabi-Yau property. We shall show that all $n$-representation-finite algebras are twisted fractionally Calabi-Yau. We also show that for any $\ell>0$, twisted $\frac{n(\ell-1)}{\ell}$-Calabi-Yau algebras of global dimension at most $n$ are $n$-representation-finite. As an application, we give a construction of $n$-representation-finite algebras using the tensor product.

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